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Spectra and Distribution Functions of Stably Stratified Turbulence

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IUTAM Symposium on Turbulence in the Atmosphere and Oceans

Part of the book series: IUTAM Bookseries ((IUTAMBOOK,volume 28))

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Abstract

We examine homogeneous stably stratified turbulence both freely decaying and randomly forced cases. Our principal focus is the scale size distribution of the eddies and waves (spectra) comprising the flow. We also present results for the rate of decay for unforced flows. The tools used in both spectral and decay studies are direct numerical simulations (DNS), combined with elements of the statistical theory of turbulence. For situationally maintained flows, our results are consistent with spectra that are steeper than Kolmogorov at large scales but fair over into the normal isotropic inertial range at smaller scales. The DNS decay rate of freely decaying strongly stratified turbulence is consistent with t −1. For stratified flow, our simulations are consistent with a near equilibration between waves and vortical eddies.

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References

  1. Nastrom, G.D., Gage, K.S., Jasperson, W.H.: Atmospheric kinetic energy spectrum, 100−104 km. Nature, 310, 36–38 (1984)

    Article  Google Scholar 

  2. Riley, J.J., Metcalfe, R.W., Weissman, M.A.: Direct numerical simulations of homogeneous turbulence in density stratified fluids. Proc. AIP Conf. on Nonlinear Properties of Internal Waves, (ed. Bruce J. West), 79–112 (1982)

    Google Scholar 

  3. Lilly, D.K.: Stratified turbulence and the mesoscale variability of the atmosphere. J. Atmos. Sci. 40, 749–761(1983)

    Article  Google Scholar 

  4. Majda, A.J., Grote, M.J.: Model dynamics and collapse in decaying strongly stratified flows. Phys. Fluids 9 (10), 2932–2940 (1997)

    Article  Google Scholar 

  5. Herring, J.R., Métais, O.: Numerical experiments in forced stably stratified turbulence. J. Fluid Mech. 202, 97–115 (1989)

    Article  Google Scholar 

  6. Lilly, D.K.: Numerical simulation of developing and decaying two-dimensional turbulence. J. Fluid Mech. 45, 395–415 (1971)

    Article  Google Scholar 

  7. Rotta, J.: Statistische Theorie nichthomogener Turbulenz. Z. Phys. 129, 127–147 (1951)

    Google Scholar 

  8. Herring, J.R., Kimura, Y., James, R., Davidson, P., Clyne, J.: Statistical and Dynamical Questions in Stratified Turbulence, in Mathematical and Physical Theory of Turbulence, Proceedings of the 2002 International Turbulence Workshop, J. Cannon and B. Shivamoggi Eds., Chapman & Hall/CRC, Taylor & Francis Group, Boca Raton London New York (2006)

    Google Scholar 

  9. Métais, O., Herring, J.R.: Numerical studies of freely decaying homogeneous stratified turbulence. J. Fluid Mech. 202, 117–148 (1989)

    Article  Google Scholar 

  10. Fincham, A.M., Maxworthy, T., Spedding, G.R.: The horizontal and vertical structure of the vorticity field in freely-decaying, stratified grid–turbulence. Preprints, 4 th Symposium on Stratified Flows Vol. 2, Sec. A4 (1994)

    Google Scholar 

  11. Kimura, Y., Herring, J.R.: Energy spectra of stably stratified turbulence. Preprint, to be submitted to J. Fluid Mech. (2010)

    Google Scholar 

  12. Kaneda, Y., Ishida, T.: Suppression of vertical diffusion in strongly stratified turbulence. J. Fluid Mech. 402, 311–327 (2000)

    Article  Google Scholar 

  13. Kimura, Y., Herring, J.R.: Diffusion in stably stratified turbulence. J. Fluid Mech. 328, 253–263 (1996)

    Article  Google Scholar 

  14. Holloway, G.: The buoyancy flux from internal gravity wave breaking. Dyn. Atmos. Oceans 12, 107–125 (1988)

    Article  Google Scholar 

  15. Carnevale, C., Briscolini, M. & Orlandi, P.: Buoyancy-to-inertial-range transition in forced stratified turbulence. J. Fluid Mech. 427, 205–239 (2001)

    Article  Google Scholar 

  16. Linborg, E.: The energy cascade in a strongly stratified fluid. J. Fluid Mech. 550, 207–242 (2006)

    Article  Google Scholar 

  17. Brethouwer, G., Billant, P., Lindborg, E., Chomaz, J.-M.: Scaling analysis and simulation of strongly stratified turbulent flows. J. Fluid Mech. 585, 343–368 (2007)

    Article  Google Scholar 

  18. Godeferd, F.S., Cambon, C.: Detailed investigation of energy transfer in homogeneous stratified turbulence. Phys. Fluids 6 (6), 2084–2100 (1994)

    Article  Google Scholar 

  19. Sukoriansky, S., Galperin, B.: Nonlinear Processes in Geophysics. Proc. London Math. Soc. 20, 10–25 (2006)

    Google Scholar 

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Correspondence to Jackson R. Herring .

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Herring, J.R., Kimura, Y. (2010). Spectra and Distribution Functions of Stably Stratified Turbulence. In: Dritschel, D. (eds) IUTAM Symposium on Turbulence in the Atmosphere and Oceans. IUTAM Bookseries, vol 28. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0360-5_12

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  • DOI: https://doi.org/10.1007/978-94-007-0360-5_12

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-0359-9

  • Online ISBN: 978-94-007-0360-5

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